More by Saharon Shelah

Abstract

We shall prove that if a model of cardinality $\kappa$ can be expanded to a model of a sentence $\psi$ of $L_{\lambda^+,\omega}$ by adding a suitable predicate in more than $\kappa$ ways, then, it has a submodel of power $\mu$ which can be expanded to a model of $\psi$ in $> \mu$ ways provided that $\lambda,\kappa,\mu$ satisfy suitable conditions.